The present work introduces a transient endoreversible model of a heat-driven refrigeration plant, which is driven by a fuel-burning heater. The model consists of a combustion chamber with negligible heat loss to the ambient, a refrigerator with three finite-size heat exchangers, namely, the evaporator between the refrigeration load and refrigerant, the condenser between the refrigerant and the ambient, and the generator between the combustion chamber and the refrigerant, and finally the refrigerated space. The total thermal conductance of the three heat exchangers is fixed. A thermodynamic optimization of the absorption cycle is then performed, reporting the operating conditions for minimum time to reach a prescribed cold-space temperature, thus maximum refrigeration rate, specifically, the optimal mass fuel flow rate and the optimal way of allocating the thermal conductance inventory. Half of the total supply of thermal conductance has to be divided equally between the generator and evaporator and the other half allocated to the condenser, for optimal operation. A narrow range of fuel flow rates lead to the minimum time to achieve a prescribed cold-space temperature, thus stressing the importance of the transient analysis. Appropriate dimensionless groups were identified and the generalized results are reported in dimensionless charts.